FA-93541 / Solar tracker geometry / Open access
Tracker actuator step command: deadband uses clamped target · case 01
A tracker sitting just inside its stop hunts when the raw target is far outside the limits.
ROOT CAUSE
The deadband is evaluated against the unclamped target.
VERIFIED REPAIR
Evaluate the deadband against the clamped target error.
Unsuccessful approach: Skipping the deadband for out-of-range targets makes the actuator chatter at the stop.
Case contract
Angles in millidegrees. The target is clamped to [lo, hi]. If |target - current| < deadband no move is made. Otherwise the move is limited to +-max_step, converted to whole motor steps of dps millidegrees truncated toward zero. Return [new position, signed steps].
Why this case matters
Single-axis and dual-axis solar trackers turn a sun direction into actuator commands; a sign, frame or limit mistake points a whole plant away from the sun or into a mechanical stop.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(target, current, deadband, max_step, dps, lo, hi):
tgt = min(max(target, lo), hi)
err = tgt - current
if abs(target - current) < deadband:
return [current, 0]
move = max(-max_step, min(max_step, err))
steps = abs(move) // dps
if move < 0:
steps = -steps
return [current + steps * dps, steps]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-57417, -56117, 500, 2000, 300, -52000, 60000], [-54317, 6]],
['control 2', [-62089, -29689, 500, 5000, 300, -55000, 60000], [-34489, -16]],
['control 3', [-4975, 2618, 1000, 5000, 7, -55000, 60000], [-2380, -714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [48241, -7501, 500, 500, 125, -55000, 60000], [-7001, 4]],
['control 2', [53151, 50604, 0, 5000, 7, -55000, 55000], [53145, 363]],
['control 3', [54600, -48703, 1000, 2000, 125, -55000, 60000], [-46703, 16]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-63679, -20673, 250, 5000, 125, -52000, 60000], [-25673, -40]],
['control 2', [13642, -49671, 1000, 5000, 7, -52000, 55000], [-44673, 714]],
['control 3', [17787, -27002, 0, 5000, 125, -55000, 52000], [-22002, 40]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-66913, 56864, 250, 5000, 125, -52000, 52000], [51864, -40]],
['control 2', [19310, -10964, 250, 5000, 125, -52000, 52000], [-5964, 40]],
['control 3', [17837, -33972, 250, 5000, 7, -60000, 52000], [-28974, 714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [22704, 24328, 1000, 5000, 300, -60000, 55000], [22828, -5]],
['control 2', [56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]],
['control 3', [-50667, 12076, 1000, 2000, 125, -52000, 60000], [10076, -16]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| boundary: error equal to deadband | [1500, 4] | [1500, 4] | Passed |
| boundary: target past west stop | [59994, 142] | [59994, 142] | Passed |
| normal: negative move truncation | [-1800, -6] | [-1800, -6] | Passed |
| regression: far target while parked at stop | [59998, 14] | [59900, 0] | Failed |
| control 1 | [-54317, 6] | [-54317, 6] | Passed |
| control 2 | [-34489, -16] | [-34489, -16] | Passed |
| control 3 | [-2380, -714] | [-2380, -714] | Passed |
SHA-256 / 6f6ae30487291e3ba6930559ee686fe3ea401d8d948c20e94aabd99ed9dff8eb
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(target, current, deadband, max_step, dps, lo, hi):
tgt = min(max(target, lo), hi)
err = tgt - current
if abs(err) < deadband and lo <= target <= hi:
return [current, 0]
move = max(-max_step, min(max_step, err))
steps = abs(move) // dps
if move < 0:
steps = -steps
return [current + steps * dps, steps]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-57417, -56117, 500, 2000, 300, -52000, 60000], [-54317, 6]],
['control 2', [-62089, -29689, 500, 5000, 300, -55000, 60000], [-34489, -16]],
['control 3', [-4975, 2618, 1000, 5000, 7, -55000, 60000], [-2380, -714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [48241, -7501, 500, 500, 125, -55000, 60000], [-7001, 4]],
['control 2', [53151, 50604, 0, 5000, 7, -55000, 55000], [53145, 363]],
['control 3', [54600, -48703, 1000, 2000, 125, -55000, 60000], [-46703, 16]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-63679, -20673, 250, 5000, 125, -52000, 60000], [-25673, -40]],
['control 2', [13642, -49671, 1000, 5000, 7, -52000, 55000], [-44673, 714]],
['control 3', [17787, -27002, 0, 5000, 125, -55000, 52000], [-22002, 40]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-66913, 56864, 250, 5000, 125, -52000, 52000], [51864, -40]],
['control 2', [19310, -10964, 250, 5000, 125, -52000, 52000], [-5964, 40]],
['control 3', [17837, -33972, 250, 5000, 7, -60000, 52000], [-28974, 714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [22704, 24328, 1000, 5000, 300, -60000, 55000], [22828, -5]],
['control 2', [56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]],
['control 3', [-50667, 12076, 1000, 2000, 125, -52000, 60000], [10076, -16]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| boundary: error equal to deadband | [1500, 4] | [1500, 4] | Passed |
| boundary: target past west stop | [59994, 142] | [59994, 142] | Passed |
| normal: negative move truncation | [-1800, -6] | [-1800, -6] | Passed |
| regression: far target while parked at stop | [59998, 14] | [59900, 0] | Failed |
| control 1 | [-54317, 6] | [-54317, 6] | Passed |
| control 2 | [-34489, -16] | [-34489, -16] | Passed |
| control 3 | [-2380, -714] | [-2380, -714] | Passed |
SHA-256 / 7b5eec2eff8e4d04ad9da728574101283259df4bf6c64d773d777d016b16fa28
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(target, current, deadband, max_step, dps, lo, hi):
tgt = min(max(target, lo), hi)
err = tgt - current
if abs(err) < deadband:
return [current, 0]
move = max(-max_step, min(max_step, err))
steps = abs(move) // dps
if move < 0:
steps = -steps
return [current + steps * dps, steps]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-57417, -56117, 500, 2000, 300, -52000, 60000], [-54317, 6]],
['control 2', [-62089, -29689, 500, 5000, 300, -55000, 60000], [-34489, -16]],
['control 3', [-4975, 2618, 1000, 5000, 7, -55000, 60000], [-2380, -714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [48241, -7501, 500, 500, 125, -55000, 60000], [-7001, 4]],
['control 2', [53151, 50604, 0, 5000, 7, -55000, 55000], [53145, 363]],
['control 3', [54600, -48703, 1000, 2000, 125, -55000, 60000], [-46703, 16]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-63679, -20673, 250, 5000, 125, -52000, 60000], [-25673, -40]],
['control 2', [13642, -49671, 1000, 5000, 7, -52000, 55000], [-44673, 714]],
['control 3', [17787, -27002, 0, 5000, 125, -55000, 52000], [-22002, 40]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [-66913, 56864, 250, 5000, 125, -52000, 52000], [51864, -40]],
['control 2', [19310, -10964, 250, 5000, 125, -52000, 52000], [-5964, 40]],
['control 3', [17837, -33972, 250, 5000, 7, -60000, 52000], [-28974, 714]]],
[['boundary: error equal to deadband', [1500, 1000, 500, 2000, 125, -60000, 60000], [1500, 4]],
['boundary: target past west stop', [80000, 59000, 250, 5000, 7, -60000, 60000], [59994, 142]],
['normal: negative move truncation', [-10000, 0, 250, 2000, 300, -60000, 60000], [-1800, -6]],
['regression: far target while parked at stop', [80000, 59900, 500, 2000, 7, -60000, 60000],
[59900, 0]],
['control 1', [22704, 24328, 1000, 5000, 300, -60000, 55000], [22828, -5]],
['control 2', [56539, -49336, 500, 2000, 7, -60000, 55000], [-47341, 285]],
['control 3', [-50667, 12076, 1000, 2000, 125, -52000, 60000], [10076, -16]]]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| boundary: error equal to deadband | [1500, 4] | [1500, 4] | Passed |
| boundary: target past west stop | [59994, 142] | [59994, 142] | Passed |
| normal: negative move truncation | [-1800, -6] | [-1800, -6] | Passed |
| regression: far target while parked at stop | [59900, 0] | [59900, 0] | Passed |
| control 1 | [-54317, 6] | [-54317, 6] | Passed |
| control 2 | [-34489, -16] | [-34489, -16] | Passed |
| control 3 | [-2380, -714] | [-2380, -714] | Passed |
SHA-256 / 85c558e85a0d221f54d66f8a0e0ddda172911ed40454c3ea2838633d6e9a615e
Verification & scope
Deterministic stipulated toy contract for teaching; no claim of conformance with any standard, vendor protocol or production controller. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:51:56.152738+00:00.
Case digest / 84fa77ca103252b57f3e1ee394f0504578ddc45663067b734ce9edd0b23aa11d